Geodesic flow for CAT(0)-groups

TL;DR

This paper introduces a flow space for CAT(0)-spaces, enabling the proof that CAT(0)-groups are transfer reducible over virtually cyclic groups, advancing the Farrell-Jones Conjecture.

Contribution

It constructs a flow space analogous to geodesic flow for CAT(0)-spaces and uses it to prove transfer reducibility of CAT(0)-groups.

Findings

CAT(0)-groups are transfer reducible over virtually cyclic groups

Flow space serves as a substitute for geodesic flow in non-Riemannian settings

Supports proof of Farrell-Jones Conjecture for CAT(0)-groups

Abstract

We associate to a CAT(0)-space a flow space that can be used as the replacement for the geodesic flow on the sphere tangent bundle of a Riemannian manifold. We use this flow space to prove that CAT(0)-group are transfer reducible over the family of virtually cyclic groups. This result is an important ingredient in our proof of the Farrell-Jones Conjecture for these groups.